Theorem simp3i 1141

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  hartogslem2  9557  harwdom  9605  divalglem6  16417  structfn  17175  strleun  17176  oppchomfval  17726  sratset  21141  srads  21143  tngip  24586  dfrelog  26526  log2ub  26911  birthdaylem3  26915  birthday  26916  divsqrtsum2  26945  harmonicbnd2  26967  lgslem4  27263  lgscllem  27267  lgsdir2lem2  27289  lgsdir2lem3  27290  mulog2sumlem1  27497  siilem2  30833  h2hva  30955  h2hsm  30956  h2hnm  30957  elunop2  31994  wallispilem3  46096  wallispilem4  46097  prstchomval  49436  cnelsubclem  49480